These eight members of the Flowers family of Ellisville, Miss., have tested positive for mutation in the CDH1 gene over the past year. Carrie Hayes Valentine, in the framed photograph, died of stomach cancer in 2013.Bryan Tarnowski for The Wall Street Journal

These eight members of the Flowers family of Ellisville, Miss., have tested positive for mutation in the CDH1 gene over the past year. Carrie Hayes Valentine, in the framed photograph, died of stomach cancer in 2013.Bryan Tarnowski for The Wall Street Journal